CHAPTER 13
Options on Futures
In this chapter, we discuss option on futures contracts. This
chapter is organized into:
1. Characteristics of Options on Physicals and Options
on Futures.
2. The Market for Options on Futures
3. Pricing of Options on Futures
4. Price Relationship Between Options on Physicals and
Options on Futures
5. Put-Call Parity for Options on Futures
6. Options on Futures and Synthetic Futures
7. Risk Management with Options on Futures
Chapter 13
1
Characteristics of Options on Physicals
and Options Futures
Recall from Chapter 12 that options are written for a prespecified amount of a pre-specified asset at a pre-specified
price that can be bought or sold at a pre-specified time
period.
Call Options
The buyer of a call option has the right but not the
obligation to purchase.
The seller of a call option has the obligation to sell.
Put Options.
The buyer of a put option has the right but not the
obligation to sell.
The seller of a put option has the obligation to purchase.
Chapter 13
2
Characteristics of Options on Physicals
and Options Futures
Prices of options on futures are closely related to prices of
options on the underlying good.
Call Option on Futures
Upon exercising a option on futures, the call owner:
– Receives a long position in the underlying futures at the
settlement price prevailing at the time of exercise.
– Receives a payment that equals the settlement price
minus the exercise price of the option on futures.
The call owner would not exercise if the futures settlement
price did not exceed the exercise price.
Upon exercise, the call seller:
– Receives a short position in the underlying futures at the
settlement price prevailing at the time of exercise.
– Pays the long trader the futures settlement price minus
the exercise price.
Chapter 13
3
Characteristics of Options on Physicals
and Options Futures
On February 1, a trader buys a call option on a MAR euro
futures contract with an exercise price of $0.44 per euro.
On February 15, the call owner decides to exercise the call
option. The futures settlement price is $.48. After
gathering all the information, the owner has:
Future settlement price
The exercise price
The euro futures maturing
Euro contract amount
= $.48
= $.44/euro
= March
= 125,000 euros
Upon exercise, the call owner:
– Receives a long position in the MAR euro futures contract.
– Receives a payment = F0 – E
$.48 - .44 (125,000) = $5000
Upon exercise, the call seller:
– Receives a short position in the euro futures.
– Pay $5,000.
The traders can offset or hold their futures positions.
Chapter 13
4
Characteristics of Options on Physicals
and Options Futures
Put Option on Futures
Upon exercising a option on futures, the put owner:
– Receives a short position in the underlying futures
contract at the settlement price prevailing at the time of
exercise.
– Receives a payment that equals the exercise price minus
the futures settlement price.
The put owner would not exercise unless the exercise
price exceeded the futures settlement price.
Upon exercise, the put seller:
– Receives a long position in the underlying futures
contract.
– Pays the exercise price minus the settlement price.
Chapter 13
5
Characteristics of Options on Physicals
and Options Futures
On April 1, a trader buys a put option on a MAY wheat
futures contract. The exercise price is $2.40/bushel and
wheat contract is for 5,000 bushels. On April 4, the owner
of the call option decides to exercise. The futures
settlement price is $2.32/bushel.
Exercise price
Wheat contract
Futures settlement price
The wheat futures matures
= $2.40/bushel
= 5,000 bushels
= $2.32/bushel.
= May
Upon exercise, the put owner:
– Receives a short position MAY Wheat futures contract.
– Receives a payment = F0 – E
$2.40-$2.32 (5,000) = $400
Upon exercise, the put seller:
– Receives a long position MAY Wheat futures contract.
– Pays $400.
The traders can offset or hold their futures positions.
Chapter 13
6
Characteristics of Options on Physicals
and Options Futures
The following table summarizes the option examples
discussed previously.
Results of Futures Option Exercises
Option
Futures Results
Cash Flows
Call
Owner holds long futures position.
Seller holds short futures position.
Owner receives F0 - E.
Seller pays F0 - E.
Put
Owner holds short futures position.
Seller holds long futures position.
Owner receives E - F0.
Seller pays E - F0.
where:
F0 = futures settlement price at time of exercise
E = exercise price of the futures option
The overall profitability of the transactions depends upon
the original premium and the prices that become available
before expiration of the option.
Chapter 13
7
The Market of Options on Futures
Figure 13.1 presents some illustrative quotations for
options on futures.
Insert figure 13.1 here
Chapter 13
8
The Market of Options on Futures
Table 13.1 shows the trading volume for options on futures
by type of commodity in the fiscal year ending September
30, 1995.
Table 13.1
Trading Volume for Futures Options
(Year Ending September 30, 2003)
Commodity Group
Number of Contracts Traded (millions)
Grain
Oilseeds
Livestock
Other Agricultural
Energy/Wood
Metals
Financial Instruments
Currencies
6.8
5.3
0.9
5.3
20.7
4.3
173.9
2.1
Total
219.2
Source: Commodity Futures Trading Commission, Annual Report, 2003.
Chapter 13
9
The Market of Options on Futures
Product Profile: The NYMEX=s Crude Oil Futures Options
Contract Size: One NYMEX light, sweet, crude oil futures contract
Strike Prices: Twenty strike prices in increments of 50 cents per barrel above and below the
at-the-money strike price. The next 10 strike prices are in increments of $2.50 above the
highest and below the lowest strike prices for a total of 61 strike prices (including the at-themoney strike price).
Tick Size: One cent per barrel ($10 per contract)
Price Quote: U.S. dollars and cents per barrel.
Contract Months: Thirty consecutive months plus long-dated futures initially listed 36, 48,
60, 72, and 84 months prior to delivery.
Expiration and final Settlement: Last trading day is three business days prior to the last
trading day for the underlying futures contract.
Trading Hours: Open outcry trading is conducted from 10:00 AM until 2:30 PM.
Daily Price Limit: None.
Chapter 13
10
The Market of Options on Futures
Product Profile: The CME=s S&P 500 Futures Options
Contract Size: One S&P 500 stock index futures contract
Strike Prices: Generally12 strikes, including the at-the-money strike. Increments between
strike price generally are 25 index points. Number of strike prices increases as expiration
approaches and increments between strike prices is reduced to a minimum of 5 index points.
Tick Size: .1 index points or $25.00.
Price Quote: Price is quoted in terms of Standard & Poor=s 500 Index.
Contract Months: Four months in the March, June, September, December cycle plus the first
two serial months not in the cycle for a total of 6 contract months.
Expiration and final Settlement: Options that expire in the March, June, September,
December cycle expire at the same time as the underlying futures contract. The two nonMarch cycle options expire on the third Friday for the contract month.
Trading Hours: Floor: 8:30 a.m. to 3:15 p.m.; Globex: Monday through Thursday 3:30 p.m.
to 8:15 a.m. with a shutdown period from 4:30 p.m. to 5:00 p.m. nightly. Sunday and holidays
5:30 p.m. to 8:15 a.m.
Daily Price Limit: Trading halted when futures trading is halted
Chapter 13
11
The Market of Options on Futures
Product Profile: The CME=s Eurodollar Futures Options
Contract Size: One Eurodollar futures contract
Strike Prices: Generally12 strikes, including the at-the-money strike. Increments between
strike price generally are 25 index points. Number of strike prices increases as expiration
approaches and increments between strike prices is reduced to a minimum of 5 index points.
Tick Size: .01 index points or $25.00.
Price Quote: Price is quoted in terms of the IMM 3-month Eurodollar index, 100 minus the
yield on an annual basis for a 360-day year.
Contract Months: Eight months in the March, June, September, December cycle plus the first
two serial months not in the cycle for a total of 10 contract months.
Expiration and final Settlement: Options on the March, June, September, December cycle
cease trading at 5:00 a.m. Chicago Time (11:00 a.m. London Time) on the second London
bank business day immediately preceding the third Wednesday of the contract month. The
two non-March cycle options expire on the Friday immediately preceding the third
Wednesday for the contract month.
Trading Hours:Floor: 7:20 a.m.-2:00 p.m; Globex: Mon/Thurs 2:10 p.m.-7:05 p.m.;
Shutdown period from 4:00 p.m. to 5:00 p.m. nightly; Sunday & holidays 5:30 p.m.-7:05 p.m.
Daily Price Limit: No limit
Chapter 13
12
Pricing Options on Futures
Recall from Chapter 12:
European Options
European options can be exercised only on the maturity
date.
American Options
American options can be exercised any time prior to
maturity.
The Black-Scholes model focus best on European options
which avoids problems with early exercise and dividends.
When there is a dividend and the dividend rate varies, the
Black-Scholes model is not suitable for valuing options on
futures.
The Black-Scholes model can be modified for forward
option pricing.
Chapter 13
13
Graphical Approach to American Options
on Futures
Figure 13.2 illustrates how European options prices are
good approximations for American futures option prices
Insert figure 13.2 here
Chapter 13
14
Black-Scholes Model for Options on
Forward Contracts
The Black-Scholes equation for option on forward
contracts is:
C=e
- rt
[ F 0,t N( d *1 ) - E N( d *2 )]
Where
r = risk-free rate of interest
t = time until expiration for the forward and the option
F0,t = forward price for a contract expiring at time t
α = standard deviation of the forward contract’s price
ln( F / E )  .5 2t
d 
 t
*
1
d * 2  d *1   t
If there were no uncertainty, N(d1*) and N(d2*) will equal
1 and the equation would simplify to:
Cf = e-rt[F0,t - E]
Chapter 13
15
European Versus American Option on
Futures
European Options
Early exercise of an option on a non-dividend paying stock
is not recommended:
– Recall that upon exercising, the call owner receives the
intrinsic value (S – E).
– Exercising a call discards the excess value of the option
over and above S – E.
American Options
Early exercise of a dividend paying futures option has
benefits and costs
– Benefit: exercise provides an immediate payment of F – E
which can earn interest until expiration ert [F - E].
– Cost: sacrifice of option value over and above intrinsic
value F – E.
Chapter 13
16
Approximating European and American
Futures Option Values
Table 13.2 compares the theoretical values for
European and American options on futures. The table
assumes that the option on futures expires in half a year
and has an exercise price of $100. The risk-free rate of
interest is 8% and the standard deviation of the
percentage change in the futures price is 0.2.
Table 13.2
Comparison of European and Approximate American
Futures Option Call Values
r = .08
σ = .20
t = .5 years E = 100
Futures Price
European
Approximate
American
80
0.30
0.30
90
1.70
1.72
100
5.42
5.48
110
11.73
11.90
120
19.91
20.34
Source: G. BaroneBAdesi and R. Whaley, AEfficient Analytic Approximation of
American Option Values,@Journal of Finance, 42:2, June 1987, pp. 301B320.
Chapter 13
17
Efficiency of The Option on Futures
Market
Most tests of efficiency examine whether market prices
match the prices of a theoretical model.
A test of market prices against a theoretical model is a joint
test of the market's efficiency and the model's ability to
correctly represent the price.
The results of Whaley’s test for efficiency are presented in
Table 13.3.
Table 13.3
Pricing Discrepancies for S&P 500 Futures Options
Observed Market Price C Theoretical Price
Summary of average pricing errors of American futures option pricing models by the option's moneyness
(F/E) and by the option's time to expiration in weeks (t) for S&P 500 futures option transactions during the
period January 28, 1983, through December 30, 1983.
Calls
t<6
Puts
6 t < 12
t 12
All t
t<6
6 t < 12
t 12
All t
F/E < 0.98 B0.0630
B0.1372
B0.0872
B0.1028
B0.1064
B0.0914
B0.1056
B0.1014
0.98 F/E <1.02 B0.1228
B0.0775
0.0073
B0.0924
B0.0816
B0.0196
0.1336
B0.0406
F/E 1.02 0.0577
0.1175
0.0702
0.0806
0.1286
0.1906
30.3060
0.1929
All F/E B0.0757
B0.0599
B0.0120
B0.0606
B0.0191
0.0808
0.2287
0.0537
Source: R. Whaley, AValuation of American Futures Options: Theory and Empirical Tests,@Journal of
Finance, March 1986, p. 138.
The differences between the theoretical and market price
are significant here.
Chapter 13
18
Efficiency of The Option on Futures
Market
Some of the studies summarized in Table 13.4 compare
actual prices with Black model prices.
Table 13.4
Tests of Efficiency for Futures Options
Study
Key Results
Whaley (1986)
For S&P 500 futures options, market and theoretical
prices are systematically different.
Jordan, McCabe, and
Kenyon (1987)
For soybeans, compared the difference between actual
market prices and the Black model price, with average
differences being 4/100 of a cent per bushel.
Ogden and Tucker
(1987)
For currencies, futures options appear to be efficiently
priced.
Bailey (1987)
For gold, futures options appear to be efficiently priced.
Blomeyer and Boyd
(1988)
In early trading of TBbond futures options, inefficiencies
may have existed. However, inefficient prices were rare
and difficult to exploit.
Wilson and Fung
(1988)
For grain futures options, prices closely conformed to
the Black model. In periods of high volatility, actual
prices did not rise as much as Black model prices.
Chapter 13
19
Price Relationship Between Options on
Physicals and Options on Futures
In this section, the pricing relationship between options on
physicals and options on futures is considered, specifically
for call options. The analysis is organized as follows:
1. European options
2. American options on underlying assets with no cash
flow
3. American options on underlying assets with cash flow
Chapter 13
20
Price Relationship Between Options on
Physicals and Options on Futures
The following assumption will be held for this analysis:
1.
The options have the same expiration and exercise
price.
2.
The options are on the same underlying commodity.
– One option is on the commodity itself.
– One option is on the futures on the commodity.
Chapter 13
21
European Options on Physicals and
Futures
Recall from Chapter 12 that at expiration a call option on
the physical will be worth:
S-E
For European options on futures, exercise can occur only
at expiration, so it must be that:
Ft,t - E = St - E
For European options the exercise value for options on
physicals and options on futures is the same.
Chapter 13
22
American Options on Physicals and
Futures with No Underlying Cash Flows
For American options, any difference in value between
options on physicals and options on futures results from the
early exercise privilege. Table 13.5 shows the exercise
values that the option on the futures can have given the
option on physicals in percentage terms. The risk-free rate
is assumed to be 15% and the percentage change in the
underlying assets is .25.
Table 13.5
Percentage Difference in Value
for Call Options on Futures and Options on Physicals
Assumptions:
Underlying asset has no cash flows.
r = .15
σ = .25
Ratio of Physical Price to
Days Until Expiration
Exercise Price
30
60
90
180
270
0.8
0.00
0.00
0.00
1.20
2.02
0.9
0.00
0.00
0.47
1.58
3.15
1.0
0.29
0.56
1.02
2.48
4.51
1.1
0.61
1.15
1.72
3.79
6.34
1.2
1.22
2.13
2.89
5.52
8.70
Source: M. Brenner, G. Courtadon, and M. Subrahmanyam, AOptions on the Spot
and Options on Futures,@Journal of Finance, 40:5, 1985, pp. 1303-1317.
Chapter 13
23
American Options on Physicals and
Futures with Underlying Cash Flows
This analysis is particularly relevant to options on stock
indexes and options on stock index futures.
Cash flows from the underlying good reduce its value.
– When stock pays a dividend, the stock price drops by
approximately the amount of the dividend.
These cash flows affect both the option on the physical
and the option on the futures.
The analysis focuses on underlying physical asset paying
a continuous dividend (cash flow) equal to the risk-free rate
of interest.
Under conditions of certainty, a futures call option is worth
the present value of:
F0,t – E, t = 0
Based on the perfect markets Cost-of-Carry Model the
futures price will be:
F0,t = S0(1 + C)
Chapter 13
24
American Options on Physicals and
Futures with Underlying Cash Flows
For financial futures, the cost of carry is the risk-free
interest rate. Assume a continuous dividend equal to the
risk-free rate of interest. In this case, the cost of carry is
zero, so the futures call option price equals:
F0,t = S0erte-rt = S0
Substituting the value of F0,t into the Black-Scholes OPM
gives an adjusted Black-Scholes OPM of:
C f = e rt [ S 0 N( d*1 )  EN( d*2 )]
where:
Cf = the price of a call option on the futures
After adjusting the Black-Scholes model for continuous
paying dividend:
C f = e-rt S 0 N( d *1 ) - e - rt EN( d *2 )
C f = e-rt S 0 N( d 1 ) - EN( d 2 )
The values for the call option on the futures and physical are
the same. That is, d1* = d1, and d2* = d2.
Chapter 13
25
Relative Prices of Options on Physicals
and Futures
The implications of this analysis for various dividend rates
are:
Relative Prices of Options on Physicals and Futures
Option Characteristics
European Options
American Option–No Dividend
American Option–Continuous Dividend
Dividend Rate < Interest Rate
Dividend Rate = Interest Rate
Dividend Rate > Interest Rate
where:
Cf, Cp
Pf, Pp
Call
Cf = Cp
Cf > Cp
Put
Pf = Pp
Pf < Pp
Cf > Cp
Cf = Cp
Cf < Cp
Pf < Pp
Pf = Pp
Pf > Pp
= call on the futures and call on the physical
= put on the futures and put on the physical
Chapter 13
26
Put-Call Parity for Options on Futures
Recall that Put-Call Parity specifies a relationship between
the price of call and put options.
For non-dividend paying assets put-call parity equals:
C - P = S0 - Ee-rt
where:
C
P
E
S0
r
t
=
=
=
=
=
=
value of a call with exercise price E
value of a put with exercise price E
exercise price of both the call and put
stock price
risk-free rate of interest
time until the options expire
Chapter 13
27
Put-Call Parity for Options on Futures
Before expiration, for options on futures, the relationship
can be expressed as:
Cf - Pf = (F0,t - E)e-rt
where:
Cf
= futures call option with exercise price E
Pf
= futures put option with exercise price E
F0,t
= current futures price
E
= common exercise price for Cf and Pf
r
= risk-free rate
t
= time until expiration for the futures and options
Comparing both equations shows the similar structure of
put-call parity for options on physicals and on futures.
Chapter 13
28
Put-Call Parity for Options on Futures
Using continuous compounding, the Cost-of-Carry Model
for a perfect market is:
F0,t = S0ert
Substituting this expression for the futures price into the
above equation gives:
Cf - Pf = (S0ert - E)e-rt = S0 - Ee-rt
Chapter 13
29
Options on Futures and Synthetic
Futures
Synthetic Futures
A position that duplicates the profits and losses from a
futures, but consists of positions in other instruments.
Creating synthetic futures equals:
Futures Call - Futures Put = Synthetic Futures
Table 13.6 summarizes the rules for constructing synthetic
positions.
Table 13.6
Rules for Creating Synthetic Instruments
Synthetic Futures
Synthetic Call
Synthetic Put
Synthetic Short Futures
Synthetic Short Call
Synthetic Short Put
= Call
= Put
= Call
= Put
= B Put
= B Call
B Put
+ Futures
B Futures
B Call
B Futures
+ Futures
Note: A synthetic instrument has the same profit and loss characteristics as the
actual instrument. However, the synthetic instrument does not necessarily have
the same value as the actual instrument.
Chapter 13
30
Risk Management with Options on
Futures
This section explores examples related to risk
management including:
– Portfolio Insurance
– Synthetic Portfolio Insurance and Put-Call Parity
– Risk and Return in Insured Portfolios
Chapter 13
31
Risk Management with Options on
Futures Example
Assume: a stock index is currently at $100. Stocks in the
index pay no dividends, and the expected return on the
index is 10% with a standard deviation of 20%. A put option
on the index with an exercise price of $100 is available and
costs $4. Consider three investment strategies:
Portfolio A :
(uninsured)
Buy the index; total investment $100.
Portfolio B:
(half insured)
Buy the index and one-half of a put; total
investment $102.
Portfolio C:
(fully insured)
Buy the index and one put; total
investment $104.
At expiration, the three portfolios will have profits and
losses computed using the following equations:
Portfolio A:
Index Value - $100
Portfolio B:
Index Value + .5 MAX{0, Index Value –
$100} - $102
Portfolio C:
Index Value + MAX{0, Index Value –
$100} - $104
Chapter 13
32
Risk Management with Options on
Futures
Figure 13.4 graphs the profits and losses of these 3
portfolios.
Insert Figure 13.4 here
Chapter 13
33
Portfolio Insurance
Recall that in portfolio insurance, a trader transacts to
insure that the value of a portfolio does not fall below a
given amount.
Based on figure 13.4, portfolio C is an insured portfolio:
The value of portfolio C cannot fall below $100. To create
portfolio C, a trader bought the index at $100 and bought an
index put with an exercise price of $100.
The worst possible loss on portfolio C is $4. Portfolio C
must always be worth at least $100 because the value can
not fall below $100, so it an insured portfolio.
Chapter 13
34
Synthetic Portfolio Insurance and PutCall Parity
Recall that a synthetic call could be created from a long
position in the underlying good plus a long put. Thus a
synthetic call is:
Synthetic Call = Put + Index
From Figure 13.4, the Put + Index portfolio has the same
profits and losses as a call option with an exercise price of
$100.
Applying the put-call parity equation to the index example:
Call = Put + Index - Ee-rt
where:
E = exercise price on the index option
An instrument with the same value and profits and losses
as a call can be created by holding a long put, long index,
and borrowing the present value of the exercise price.
Chapter 13
35
Synthetic Portfolio Insurance and PutCall Parity
Synthetic Calls and Put-Call Parity
Synthetic Call = Put + Index
Put-Call Parity:
Call = Put + Index - E-rt
A synthetic call replicates the
profits and losses from the call, but
it does not have the same value as
the call.
The long put/long index/short bond
portfolio duplicates the value and
profits and losses of the call
option.
From the put-call parity, there is another way to create a
portfolio that exactly mimics the insured portfolio’s value at
expiration.
Call + E-rt = Put + Index
We can hold a long call plus investing the present value of
the exercise price in the risk-free asset.
Chapter 13
36
Risk’s Return on Insured Portfolios
Each of the portfolios A-C has different risk characteristics.
To explore the risk properties of the portfolios assume that
the return on the index follows a normal distribution with a
mean of 10% and a standard deviation of 20%.
Terminal Values for Portfolios A-C.
The portfolio values at expiration depend on the price of
the index at expiration. For each, the terminal value is:
Portfolio A = Index
Portfolio B = Index + MAX{0, .5(100.00 - Index)}
Portfolio C = Index + MAX{0, 100.00 - Index}
What is the probability that each of the portfolios will have
a terminal value equal to or less than $100?
Chapter 13
37
Risk Return in Insured Portfolios
Table 13.7 shows some portfolio values and the
probabilities that each portfolio will be equal to or less than
the given terminal value at the expiration date.
Table 13.7
Probability That the Terminal Portfolio Value
Will Be Equal to or Less than a Specified Value
Terminal Portfolio Value
50.00
60.00
70.00
80.00
90.00
100.00
110.00
120.00
130.00
140.00
150.00
160.00
170.00
Uninsured
Portfolio A
0.0014
0.0062
0.0228
0.0668
0.1587
0.3085
0.5000
0.6915
0.8413
0.9332
0.9773
0.9938
0.9987
Probabilities
HalfBInsured
Portfolio B
0.0000
0.0000
0.0002
0.0062
0.0668
0.3085
0.5000
0.6915
0.8413
0.9332
0.9773
0.9938
0.9987
Chapter 13
Fully Insured
Portfolio C
0.0000
0.0000
0.0000
0.0000
0.0000
0.3085
0.5000
0.6915
0.8413
0.9332
0.9773
0.9938
0.9987
38
Risk Return in Insured Portfolios
Figure 13.5 graphs the terminal portfolio values from $50
to $170 and shows the probability for each portfolio that
the terminal portfolio value will be below or equal to the
given amount.
Insert Figure 13.5 here
Chapter 13
39
Risk Return in Insured Portfolios
Returns on Portfolios A-C
Table 13.8 shows the probability that each portfolio will
achieve a return greater than a specified return.
Table 13.8
Probability of Achieving a Return
Equal to or Greater than a Specified Return
Probabilities
Portfolio Return
-0.5000
-0.4000
-0.3000
-0.2000
-0.1000
0.0000
0.1000
0.2000
0.3000
0.4000
0.5000
Uninsured
Portfolio A
HalfBInsured
Portfolio B
Fully Insured
Portfolio C
0.9987
0.9938
0.9773
0.9332
0.8413
0.6915
0.5000
0.3085
0.1587
0.0668
0.0228
1.0000
1.0000
0.9996
0.9904
0.9066
0.6554
0.4562
0.2676
0.1292
0.0505
0.0158
1.0000
1.0000
1.0000
1.0000
1.0000
0.6179
0.4129
0.2297
0.1038
0.0375
0.0107
This is a tradeoff between return and risk on the portfolios.
The portfolios having a higher return also have a higher
risk.
Chapter 13
40
Risk Return in Insured Portfolios
Figure 13.6 graphs the probabilities for each portfolio for a
range of returns from -50% to 50%.
Insert Figure 13.6 here
Chapter 13
41
Why Options on Futures
Some reasons for the popularity of options on futures are:
1. A futures position exposes a trader to a theoretically
unlimited risk of gain or loss, but this is not true for the
buyer of a futures option.
2. Options on futures dominate options on physicals in
some markets because the futures market for some
goods is much more liquid than the market for the
physical good itself.
3. Options on futures generally require less investment
than options on the physical good itself.
Chapter 13
42